z g distribution in a nutshell General pQCD picture High p T regime Low p T regime Conclusion Deciphering the z g distribution in heavy ion collisions P. Caucal, E. Iancu, A.H. Mueller and G. Soyez Institut de Physique Th´ eorique, CEA, France May 13, 2019 - Bergen Jet Tools 2019
z g distribution in a nutshell General pQCD picture High p T regime Low p T regime Conclusion Introduction I will focus mainly on the z g distribution because this allows for comparisons with results from pQCD. How to understand from first principles these measurements ? CMS Collab. PAS HIN-16-006
z g distribution in a nutshell General pQCD picture High p T regime Low p T regime Conclusion z g distribution in a nutshell Jets are first defined with anti- k T . All final particles in one jet are reclustered with Cambridge/Aachen to impose physical angular ordering. A SoftDrop declustering is used the find the first two subjets satisfying z g ≥ z cut . The angle of branching is called θ g . Larkoski, Marzani, Soyez, Thaler, 2014 One can also impose a minimal angle between the two subjets θ g ≥ θ cut . z 1 ≤ z cut z 2 ≤ z cut p T, 1 θ g ≥ θ cut z g = min ( p T, 1 ,p T, 2 ) ≥ z cut p T, 1 + p T, 2 p T, 2 p T = p T, 1 + p T, 2
z g distribution in a nutshell General pQCD picture High p T regime Low p T regime Conclusion pQCD calculation in the vacuum Sudakov form factor ∆( R , θ g ): probability to have no branching between R and θ g with z ≥ z cut . � R � 1 / 2 � � ∆ i ( R , θ g ) = exp − d θ dz P i ( z , θ ) θ g z cut P i ( z , θ ) = 2 C i α s ( zp T θ ) ¯ P i ( z ) π θ The probability density p i ( z g ) to have a given value of z g is � R p i ( z g ) = N Θ( z g − z cut ) d θ g ∆ i ( R , θ g ) P i ( z g , θ g ) θ cut
z g distribution in a nutshell General pQCD picture High p T regime Low p T regime Conclusion Jet evolution in a dense QCD medium Phys.Rev.Lett. 120 (2018) 232001 The evolution of a jet factorizes into three steps: • one angular ordered vacuum-like shower inside the medium , • medium-induced showers triggered by previous sources; • finally, a vacuum-like shower outside the medium. • Vetoed region for VLEs: essential for the factorization of VLEs from MIEs. ω ω E c θ qq VETOED ω ω ω θ θ θ 2 3 = L 4 Λ = ω c = 1 =2q qL 2 2 2 ˆ 2 1 inside θ (ω,θ) medium √ 2 θ c = ω 1 qL 3 ˆ θ c θ 1 θ 2 outside ω 2 medium ω θ
z g distribution in a nutshell General pQCD picture High p T regime Low p T regime Conclusion Primary Lund plane - Definition Density of primary emissions with a given k T = ωθ and 1 /θ . (see e.g. Dreyer, Salam, Soyez, 2018) Primary Lund Plane ( E , θ q ¯ q ) 4 V INSIDE E ω T 3 O θ 4 E D = 2 E (large z) 2 q log( k ⊥ / GeV ) INSIDE ˆ 0.1 ωθ 2 L = 2 ( ω c , θ c ) θ VETOED ωθ = Λ θ c 0 OUTSIDE OUTSIDE − 2 non-perturbative 0.01 ω c 0.1 1 10 100 2 4 6 8 ω [GeV] log(1 /θ ) large angles small angles
z g distribution in a nutshell General pQCD picture High p T regime Low p T regime Conclusion Primary Lund planes (from MC calculations) New scale for the medium-induced shower: k T = Q s ≡ √ ˆ qL . 4 4 2 4 4 1.4 1.2 3 3 3 3 q=1 GeV 2 /fm, L=4 fm, α s =0.25 q=1 GeV 2 /fm, L=4 fm, α s =0.25 1.5 VLEs only medium-induced shower 1 log(k t /GeV) log(k t /GeV) 2 2 2 2 ratio med/vac 0.8 anti-k t (R=0.4), p t =200 GeV 1 1 1 1 1 0.6 0.4 0 0 0 0 0.5 0.2 -1 -1 -1 -1 0 0 1 1 2 2 3 3 4 4 5 5 6 6 1 1 2 2 3 3 4 4 5 5 6 6 log(1/ θ ) log(1/ θ ) 4 4 1.4 4 4 2 1.2 3 3 3 3 q=1 GeV 2 /fm, L=4 fm, α s =0.25 q=1 GeV 2 /fm, L=4 fm, α s =0.25 1.5 full shower 1 med/vac ratio log(k t /GeV) log(k t /GeV) 2 2 2 2 0.8 1 1 1 1 1 0.6 0.4 0 0 0 0 0.5 0.2 -1 -1 -1 -1 0 0 1 1 2 2 3 3 4 4 5 5 6 6 1 1 2 2 3 3 4 4 5 5 6 6 log(1/ θ ) log(1/ θ )
z g distribution in a nutshell General pQCD picture High p T regime Low p T regime Conclusion Two regimes: “high p T ” and “low p T ” Lund Plane - high p T regime Lund Plane - low p T regime 6 6 4 4 z cut E E log( k ⊥ / GeV ) log( k ⊥ / GeV ) θ cut z cut E E 2 2 θ cut ( ω c , θ c ) ( ω c , θ c ) 0 0 2 4 6 8 2 4 6 8 log(1 /θ ) log(1 /θ ) z g -distribution for “ monochromatic ” gluon jets in the regimes: • “High p T ”: z cut p T ≥ ω c and θ cut ≥ θ c . Medium induced emission can not be selected by SoftDrop. • “Low p T ”: z cut p T ≤ ω c and θ cut ≥ θ c . Medium induced emissions might be selected by SoftDrop. Mehtar-Tani, Tywoniuk, 2016 • In the current LHC data, θ cut = 0 . 1 whereas in our set-up θ c ≤ 0 . 05
z g distribution in a nutshell General pQCD picture High p T regime Low p T regime Conclusion High p T regime: incoherent energy loss In the high pT regime, the only leading medium effect is the incoherent energy loss of the two subjets via medium-induced radiation. Incoherent energy loss because we chose θ g ≥ θ cut ≥ θ c . Mehtar-Tani, Salgado, Tywoniuk, 2010-1 ; Casalderrey-Solana, Iancu, 2011 Let us call E ( p T , 1 , R 1 ) the energy loss by a subjet. p T, 1 = zp T − E ( zp T , ∼ θ g / 2) θ g ≥ θ cut ≥ θ c p T , 2 = (1 − z ) p T − E ((1 − z ) p T , ∼ θ g / 2) p T
z g distribution in a nutshell General pQCD picture High p T regime Low p T regime Conclusion High p T regime: pQCD calculation Vacuum: � R p i ( z g ) = N Θ( z g − z cut ) d θ g ∆ i ( R , θ g ) P i ( z g , θ g ) θ cut � R � 1 / 2 � � ∆ i ( R , θ g ) = exp − d θ dz P i ( z , θ )Θ( z − z cut ) θ g 0
z g distribution in a nutshell General pQCD picture High p T regime Low p T regime Conclusion High p T regime: pQCD calculation Vacuum: z is the physical splitting fraction. � 1 � R p i ( z g ) = N Θ( z g − z cut ) d θ g ∆ i ( R , θ g ) P i ( z , θ g ) δ ( z − z g ) dz 0 θ cut � R � 1 / 2 � � ∆ i ( R , θ g ) = exp − d θ dz P i ( z , θ )Θ( z − z cut ) θ g 0
z g distribution in a nutshell General pQCD picture High p T regime Low p T regime Conclusion High p T regime: pQCD calculation With the medium: � 1 � R p i ( z g ) = N Θ( z g − z cut ) dz d θ g ∆ i ( R , θ g ) P i ( z , θ g ) δ ( Z g ( z , θ g ) − z g ) 0 θ cut
z g distribution in a nutshell General pQCD picture High p T regime Low p T regime Conclusion High p T regime: pQCD calculation With the medium: � 1 � R p i ( z g ) = N Θ( z g − z cut ) dz d θ g ∆ i ( R , θ g ) P i ( z , θ g ) δ ( Z g ( z , θ g ) − z g ) 0 θ cut � R � 1 / 2 � � ∆ i ( R , θ g ) = exp − d θ dz P i ( z , θ )Θ( Z g ( z , θ ) − z cut ) θ g 0 Z g ( z , θ ) = min ( zp T − E ( zp T , θ g ) , (1 − z ) p T − E ((1 − z ) p T , θ g )) p T − E ( zp T , θ g ) − E ((1 − z ) p T , θ g ) p T, 1 = zp T − E ( zp T , ∼ θ g / 2) θ g ≥ θ cut ≥ θ c p T , 2 = (1 − z ) p T − E ((1 − z ) p T , ∼ θ g / 2) p T
z g distribution in a nutshell General pQCD picture High p T regime Low p T regime Conclusion The energy loss function E ( p T , R ) The importance of the “in-medium” multiplicity of VLEs α s 2 ω c , partonic energy loss via MIEs is constant. For p T ≫ ω br ≡ ¯ For jets with VLEs and MIEs, the energy loss increases because of the VLEs multiplicity inside the medium. average energy loss average energy loss 70 45 MI only anti-k t (R=0.4) 40 MI+VLEs 60 θ max =R, k t,min =0.25 =1.5 GeV/fm 2 , L=4 fm, α - ^ q s =0.25 average energy loss [GeV] 35 average energy loss [GeV] 50 30 40 25 30 20 15 20 MI only 10 anti-k t (R), p t,0 =200 10 MI+VLEs θ max =R, k t,min =0.25 5 fit (C=4.7) =1.5 GeV/fm 2 , L=4 fm, α - 0 ^ q s =0.25 2 5 10 20 50 100 200 500 1000 0 0 0.2 0.4 0.6 0.8 1 p t0 [GeV] R Analytical estimations: DL and single emission approximation, � p T � R d θ d 2 N E ( p T , θ g ) ∝ ω br d ω d ω d θ Θ in 0 θ c
z g distribution in a nutshell General pQCD picture High p T regime Low p T regime Conclusion High p T regime: analytical and MC results Ratio med/vac - Normalized to 1 Ratio med/vac - N jets normalized 1.1 q=1.5 GeV 2 /fm, L=4 fm, p T =1 T q=1.5 GeV 2 /fm, L=4 fm, p T =1 T eV eV 1 1.08 anti-k t (R=0.4) 1.06 0.95 1.04 1.02 0.9 1 ε =11 GeV 0.85 ε =20 GeV 0.98 Monte-Carlo ε (p T )= ε 0 + ε 1 log(p T / ω c ) 0.96 0.8 0.1 0.2 0.3 0.4 0.5 0.1 0.2 0.3 0.4 0.5 z g z g Comments p T dependence of energy loss coming from VLEs leading to an increase in the number of sources. This p T dependence is important to achieve a good analytic description of both ways of normalizing z g .
z g distribution in a nutshell General pQCD picture High p T regime Low p T regime Conclusion High p T regime: analytical and MC results Ratio med/vac - Normalized to 1 Ratio med/vac - N jets normalized 1.1 q=1.5 GeV 2 /fm, L=4 fm, p T =1 T q=1.5 GeV 2 /fm, L=4 fm, p T =1 T eV eV 1 1.08 anti-k t (R=0.4) 1.06 0.95 1.04 1.02 0.9 1 ε =11 GeV 0.85 ε =20 GeV 0.98 Monte-Carlo ε (p T )= ε 0 + ε 1 log(p T / ω c ) 0.96 0.8 0.1 0.2 0.3 0.4 0.5 0.1 0.2 0.3 0.4 0.5 z g z g Comments The effects of the incoherent energy loss on z g have also been discussed in Mehtar-Tani, Tywoniuk, 2016 & Chang, Cao, Qin, 2018 These papers refers to relatively low p T . Indeed, even in that regime, this mechanism represents an ingredient of the full physical scenario.
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